The curves $\displaystyle {f{{\left({x}\right)}}}={x}^{{2}}-{4}{x}-{2}$ and $\displaystyle {g{{\left({x}\right)}}}=-{3}{x}-{2}$ intersect at the point (1,-5).

Find the acute angle of intersection, in radians on the domain $\displaystyle {0}\le{t}\le\frac{\pi}{{2}}$, to two decimal places.